Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

TL;DR

This paper analyzes the statistical mechanics of a relativistic one-dimensional self-gravitating system, deriving distribution functions and examining how relativistic effects influence system properties compared to the non-relativistic case.

Contribution

It provides the first leading-order relativistic corrections to the statistical mechanics of a 1D self-gravitating system, connecting relativistic and non-relativistic results.

Findings

Relativistic effects sharpen position and momentum distributions.

Relativistic gas has a lower temperature at fixed energy.

Results recover non-relativistic case as c approaches infinity.

Abstract

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of $N$-particles coupled to lineal gravity and can be considered as a model of $N$ relativistically interacting sheets of uniform mass. The partition function and one-particle distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.